I want to use ROOT to decompose a general (mxn) matrix via householder transformations. (m > n)
I have an object QRH of the type TDecompQRH initialised with a Matrix A that I want to decompose. I do:
and make sure it suceeded.
After that I took a look at the stored matrices Q and R and especially QR which looks quite different from the initial A. A had strict band structure and only positive elements, QR is a lot more entries, of which quite some are negative.
Looking at the header of TDecompQRH I found this as the only documentation on the class:
[quote]Decompose a general (m x n) matrix A into A = fQ fR H where
fQ : (m x n) - orthogonal matrix
fR : (n x n) - upper triangular matrix
H : HouseHolder matrix which is stored through
fUp: (n) - vector with Householder up’s
fW : (n) - vector with Householder beta’s
and a reference to a paper I don’t have accessible, which would probably explain the documentation…
Now what is H? After all I read about the QR decomposition of a matrix one should have a series of householder matrices Q_i forming a final matrix Q and, in addition, the upper triang. matrix R.
I have built H from fUp and fW but can’t make any sense out of it. Is there anything else to do?
Thanks for any hints…